Quantum anchor:U q (sl(2)) case

We introduce the tangent spaceT(H _q ) on the quantum hyperboloid (A _0,q ^c ) and equip it with an action onA _0,q ^c being a deformation of the action of vectors fields on functions. An embeddingsl(2) _q →T(H _q ) ofq-deformed Lie algebrasl(2) being an analogue of the anchorsl(2)→Vect (H) is called “quantum anchor”.